@Alejandro Jakubi Alejandro this is something like the 3rd time in as many weeks that you have used applyrule to nice effect, deftly providing a more general solution.

This is great because applyrule deserves more notice, if not as a bug-free command then certainly as representative of a symbolic problem-solving methodology. (And heavier use can lead to more bug reports on it, which can ideally lead to it getting stronger. It has its share of weaknesses.)

Sometimes I think that Maple could learn more from Mathematica, in broad terms of how patterns are utilized. I'm not saying that Maple never uses patterns -- maybe see inttrans for example.

It's not really related to the posted topic but I'm reminded of something Alec once wrote here. I can't find the particular post, so I'll make up an example. The essence was that a human can immediately find a candidate explicit solution (namely, 1/4) of something like the following. But `solve` returns only an implicit RootOf:

> expr:=arcsin(exp(erfc(x))-x);
expr := -arcsin(-exp(erfc(x)) + x)

> eval(expr,x=1/4);
arcsin(exp(erfc(1/4)) - 1/4)

> solve(expr=eval(expr,x=1/4),x);
exp(RootOf(_Z - erfc(exp(_Z) - exp(erfc(1/4)) + 1/4))) - exp(erfc(1/4)) + 1/4

> evalf(%);

Please Wait...